Much of the talk is rooted in notions that have hardened into political truths: that a vice president can boost the top of the ticket by adding ethnic or geographic balance. Maybe they can even help the presidential nominee carry their home state.

Political scientists Christopher Devine and Kyle Kopko have a new book, “The VP Advantage: How Running Mates Influence Home State Voting in Presidential Elections,” that explores and debunks some of those notions.

In an interview, Devine, who teaches at the University of Dayton in Ohio, and Kopko, an assistant dean at Elizabethtown College in Pennsylvania, also offered some advice to Hillary Clinton and Donald Trump, should they seek help in choosing their No. 2.

One argument you hear for picking a vice presidential prospect is their ability to “carry” their home state, or put a noncompetitive state into play. But you say it hasn’t worked that way.

Christopher Devine: That’s right – with a caveat. Generally speaking, presidential tickets do not perform any better in the home state of the running mate. In our book, we tested the “vice presidential home-state advantage” using three distinct empirical methods, and each returned that same result; on average, the advantage is not statistically distinguishable from zero.

However, we do find a significant electoral advantage in the rare case that a vice presidential candidate meets these two conditions: First, comes from a small state, in terms of population; second, has served the people of that state as an elected official for a long time.

A great example of an experienced candidate from a small state is Joe Biden, who we find delivered a measurable advantage in Delaware when running for vice president. Essentially, a Biden-esque running mate is an “institution” in his home state, familiar and beloved enough to actually change how some people vote for president.

But there’s the rub – small states like Delaware have few electoral votes, so they’re unlikely to swing an election. That’s why, historically speaking, we feel confident saying that the vice presidential home-state advantage has been inconsequential – because, on the rare occasion that it happens, it doesn’t affect the outcome of the election.

Is a vice presidential pick any more likely to help with a particular ethnic or demographic group?

Devine: No, based on our research. Recently, we analyzed survey results from election years in which a vice presidential candidate came from a politically underrepresented group: women (Geraldine Ferraro in 1984, Sarah Palin in 2008), as well as religious minorities including Catholics (Sargent Shriver in 1972, Ferraro in 1984, Biden in 2008 and Paul Ryan in 2012) and Joe Lieberman, who is Jewish, in 2000. We wanted to see if people from the same demographic group were more likely than normal to vote for the presidential ticket in those years.

Generally speaking, they were not. Women were no more likely to vote for Ferraro’s Democratic ticket in 1984 or Sarah Palin’s Republican in 2008 than in other election years.

We find mostly the same results in terms of religious minorities. Based on these results, it’s unlikely that, say, Hillary Clinton would win more votes from Latinos simply by picking HUD Secretary Julian Castro or [Los Angeles] Congressman Xavier Becerra. She might perform better among Latinos for other reasons, though, such as opposition to Donald Trump’s candidacy.

If you were to offer a set of criteria, a sort of how-to-pick-a-vice-president-for-dummies, what would they be?

Kyle Kopko: First and foremost, a vice presidential candidate should be able to serve as president in the event of a president’s death, incapacitation, resignation or impeachment. It would be an incredible disservice to the country if someone was selected as vice president merely for a perceived electoral advantage and ultimately could not effectively act as president in the event of an unforeseen crisis.

Second, a vice president should be someone the president can work with on a day-to-day basis to advance policy; having a good rapport with a vice presidential candidate will be important.

Third, it would be helpful if a vice president can balance the ticket in terms of political experience or policy expertise. In recent decades, vice presidents have increasingly played the role of a policy advisor to presidents. Selecting a running mate who can offer sound advice will serve the presidential candidate well once in office.

Can you point to an example of a successful vice presidential pick? How about a worst pick?

George W. Bush picking Dick Cheney and Barack Obama picking Joe Biden are two good examples of this. In both cases, relatively inexperienced presidential candidates selected running mates with extensive experience, particularly in foreign policy, and there’s good reason to believe that voters were reassured by those selections. For that matter, once in office Cheney and Biden were extraordinarily successful, if you measure vice presidential success in terms of influence within the administration.

You’ll notice that we don’t mention Lyndon Johnson in 1960 as an example of electoral success. We devote a chapter of our book to debunking the myth that LBJ delivered Texas and the South for John F. Kennedy, based on a first-of-its-kind analysis of survey data from actual voters in that election year. In short, opinions of LBJ were no more favorable, and no more likely to influence how people voted, among voters in his home state and region versus elsewhere in the U.S.

For a worst pick, it’s hard to top Thomas Eagleton in 1972, since he was the only running mate to be subsequently removed from the ticket.

Richard Nixon’s selection of Spiro Agnew also turned out quite poorly, given that Agnew in 1973 became the only vice president to resign from office in the modern era. However, he is regarded as one of the better “attack dogs” in vice presidential history, so one could argue that Agnew also served Nixon well in some ways.

You suggest that Al Gore could have won the 2000 election had he selected another running mate. Can you explain?

Kopko: Our data indicate that vice presidential home-state advantages are highly conditional – they occur when a candidate hails from a state with a small population and the candidate has significant elected experience within that state.

Because the 2000 election was so close, had any state switched from George W. Bush to Al Gore, Gore would have won the election. That year, Al Gore’s campaign leaked his shortlist in advance of announcing Joe Lieberman’s selection. Jeanne Shaheen, New Hampshire’s then-governor (and now U.S. senator), was on Gore’s shortlist.

Shaheen fit the profile of a running mate who could deliver a home-state advantage: Her state was one of the least populous in the U.S., and she had served its people for many years in elected office. Moreover, New Hampshire was the only state in New England carried by the Bush campaign, and in that same election, Shaheen won a third term as governor of New Hampshire.

By our estimates, had Gore selected Shaheen instead of Lieberman, Gore would have carried New Hampshire by at least one point. New Hampshire would have secured a majority of Electoral College votes for Al Gore. This assumes, of course, that the dynamics of the national election would not have dramatically changed if Shaheen would have been Gore’s running mates instead of Lieberman.

If Clinton and Trump were to ask for your advice, what would you tell them?

Kopko: Aside from selecting someone who could potentially serve as president, each candidate should carefully consider their own political strengths and weaknesses when evaluating potential running mates.

Donald Trump, for example, has repeatedly referenced his status as a Washington outsider and his desire to select a running mate with political experience to help guide legislation through Congress. Several individuals fit that profile and have also been on friendly terms with Trump, including former Speaker of the House Newt Gingrich, Sen. Jeff Sessions [of Alabama], and Oklahoma Gov. Mary Fallin.

Given the controversial nature of Trump’s candidacy, he has a smaller pool of potential running mates compared to past Republican presidential candidates.

Hillary Clinton, on the other hand, has a wealth of political experience and it’s not essential that she select someone with similar experience. Instead, much depends on Clinton’s personal goals.

For example, if she’s hoping to shape the Democratic Party for years to come, she could select a relatively young running mate who could potentially run for president in 2024 or beyond. Castro or Perez would fit that profile, and these potential candidates would further cement the historic nature of a Clinton presidency – either would be the first major-party Latino vice presidential candidate.

If Clinton wants to advance policy that will appeal to disaffected Bernie Sanders supporters, then selecting someone like Warren or Sen. Sherrod Brown [of Ohio] could be a wise selection. Each appeals to the populous and more liberal wings of the Democratic Party.

Clinton could also select Kaine, who is a relatively centrist Democrat with experience as an executive and a legislator, as well as a national party chairman. Of course, we disagree with claims that Kaine would be likely to deliver the swing state of Virginia.

However, Kaine does satisfy what we consider the most important criterion when selecting a vice presidential candidate: He could be an effective partner in governance as vice president, and he is qualified to take over as president if needed. Other potential running mates, on both sides, fit that bill.

If Clinton and Trump are wise, it will be those candidates who populate their shortlists – rather than gimmicks and “game changers.”